[1]韩琦悦,李春花*.一类非线性薛定谔方程解的衰减估计[J].延边大学学报(自然科学版),2020,46(01):24-27.
　HAN Qiyue,LI Chunhua*.Decay estimates of solutions to a class of nonlinear Schr?dinger equations[J].Journal of Yanbian University,2020,46(01):24-27.
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一类非线性薛定谔方程解的衰减估计

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第46卷 期数: 2020年01期 页码: 24-27 栏目: 基础科学研究 出版日期: 2020-05-26
Title:
Decay estimates of solutions to a class of nonlinear Schr?dinger equations
文章编号:
1004-4353(2020)01-0024-04
作者:
韩琦悦;  李春花*
( 延边大学 理学院, 吉林 延吉 133002 )
Author(s):
HAN Qiyue;  LI Chunhua*
( College of Science, Yanbian University, Yanji 133002, China )
关键词:
非线性薛定谔方程;  次临界非线性项;  强耗散条件;  衰减估计
Keywords:
nonlinear Schr?dinger equation;  subcritical nonlinearity;  strong dissipative condition;  decay estimate
分类号:
O175.29
文献标志码:
A
摘要:
研究了一类具有次临界非线性项的薛定谔方程的大初值问题.在强耗散条件下,分析了非线性薛定谔方程itv+1/22xv=λ|v|p -1v+ia/((1+t)(p-1))v整体解的L2衰减估计,所得结果完善了文献[4]的结论.
Abstract:
We consider the large initial problem for a class of nonlinear Schr?dinger equations with subcritical nonlinearities. Under a strong dissipative condition, L2 decay estimates of global solutions to the nonlinear Schr?dinger equation itv+1/22xv=λ|v|p -1v+ia/((1+t)(p-1))v are shown. Theresearch result supplement the results of the literature [4].

参考文献/References:

[1] AGRAWAL G P. Nonlinear Fiber Optics[M]. New York: Academic Press, 1995.
[2] OHTA M, TODOROVA G. Remarks on global existence and blowup for damped nonlinear Schr?dinger equations[J]. Discrete and Continuous Dynamical Systems, 2009,23(4):1323-1325.
[3] JIN G, JIN Y, LI C. The initial value problem for nonlinear Schr?dinger equations with a dissipative nonlinearity in one space dimension[J]. Journal of Evolution Equations, 2016,16(4):983-995.
[4] YUAN X T, LI C H. The effect of gain and strong dissipative structures on nonlinear Schr?dinger equations in optical fiber[J]. Advances in Mathematical Physics. https://doi.org/10.1155/2019/7297090.{itv+1/22xv=λ|v|p -1v+ia/((1+t)(p-1))v,
v(0,x)=v0(x)(2)

相似文献/References:

[1]马瑞,李春花.一类具有位势的二维非线性薛定谔系统解的渐近行为[J].延边大学学报(自然科学版),2021,47(04):283.
　MA Rui,LI Chunhua.Asymptotic behavior of solutions to nonlinear Schrdinger systems with potentials in 2D[J].Journal of Yanbian University,2021,47(01):283.
[2]郭佳鑫,李春花.二维耗散非线性薛定谔方程解的时间衰减估计[J].延边大学学报(自然科学版),2023,(04):283.
　GUO Jiaxin,LI Chunhua.Time decay estimates of solutions to dissipative nonlinear Schr?dinger equations in two space dimensions[J].Journal of Yanbian University,2023,(01):283.

备注/Memo

收稿日期: 2020-02-16
基金项目: 吉林省教育厅项目(JJKH20180892KJ)
*通信作者: 李春花(1977—),女,副教授,研究方向为偏微分方程.

更新日期/Last Update: 2020-05-26